LMFDB - Group of Dirichlet characters of modulus 6930

sage:H = DirichletGroup(6930)

pari:g = idealstar(,6930,2)

Character group

sage:G.order() pari:g.no
Order	=	1440
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{60}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{6930}(1541,\cdot)$, $\chi_{6930}(1387,\cdot)$, $\chi_{6930}(2971,\cdot)$, $\chi_{6930}(2521,\cdot)$

First 32 of 1440 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$	$47$
$\chi_{6930}(1,\cdot)$	6930.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6930}(13,\cdot)$	6930.je	60	no	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{60}\right)$
$\chi_{6930}(17,\cdot)$	6930.io	60	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{47}{60}\right)$
$\chi_{6930}(19,\cdot)$	6930.hv	30	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{1}{15}\right)$
$\chi_{6930}(23,\cdot)$	6930.ev	12	no	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$
$\chi_{6930}(29,\cdot)$	6930.hr	30	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{15}\right)$
$\chi_{6930}(31,\cdot)$	6930.gg	30	no	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{19}{30}\right)$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{30}\right)$
$\chi_{6930}(37,\cdot)$	6930.ip	60	no	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{31}{60}\right)$
$\chi_{6930}(41,\cdot)$	6930.hp	30	no	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{6930}(43,\cdot)$	6930.fc	12	no	$1$	$1$	$e\left(\frac{1}{12}\right)$	$i$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{6930}(47,\cdot)$	6930.ix	60	no	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{15}\right)$	$i$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{6930}(53,\cdot)$	6930.if	60	no	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{3}{10}\right)$	$i$	$e\left(\frac{23}{60}\right)$
$\chi_{6930}(59,\cdot)$	6930.hc	30	no	$1$	$1$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{30}\right)$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{30}\right)$
$\chi_{6930}(61,\cdot)$	6930.hn	30	no	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{13}{15}\right)$	$1$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{30}\right)$
$\chi_{6930}(67,\cdot)$	6930.ex	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{6930}(71,\cdot)$	6930.dp	10	no	$-1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{7}{10}\right)$
$\chi_{6930}(73,\cdot)$	6930.ie	60	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{11}{60}\right)$
$\chi_{6930}(79,\cdot)$	6930.hi	30	no	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$-1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{30}\right)$
$\chi_{6930}(83,\cdot)$	6930.jc	60	no	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{6930}(89,\cdot)$	6930.dj	6	no	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{6930}(97,\cdot)$	6930.ia	60	no	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{60}\right)$
$\chi_{6930}(101,\cdot)$	6930.hh	30	no	$-1$	$1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{6930}(103,\cdot)$	6930.iv	60	no	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{6930}(107,\cdot)$	6930.jb	60	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{2}{5}\right)$	$i$	$e\left(\frac{49}{60}\right)$
$\chi_{6930}(109,\cdot)$	6930.df	6	no	$-1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{6930}(113,\cdot)$	6930.jf	60	no	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{59}{60}\right)$
$\chi_{6930}(127,\cdot)$	6930.fk	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{9}{20}\right)$
$\chi_{6930}(131,\cdot)$	6930.bx	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{6930}(137,\cdot)$	6930.ik	60	no	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{6930}(139,\cdot)$	6930.gt	30	no	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{14}{15}\right)$
$\chi_{6930}(149,\cdot)$	6930.hb	30	no	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$
$\chi_{6930}(151,\cdot)$	6930.gd	30	no	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{5}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$6930$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{60}\)
Order	$1440$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)	\(47\)
\(\chi_{6930}(1,\cdot)\)	6930.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6930}(13,\cdot)\)	6930.je	60	no	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{6930}(17,\cdot)\)	6930.io	60	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{47}{60}\right)\)
\(\chi_{6930}(19,\cdot)\)	6930.hv	30	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{6930}(23,\cdot)\)	6930.ev	12	no	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)
\(\chi_{6930}(29,\cdot)\)	6930.hr	30	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{15}\right)\)
\(\chi_{6930}(31,\cdot)\)	6930.gg	30	no	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{30}\right)\)
\(\chi_{6930}(37,\cdot)\)	6930.ip	60	no	\(-1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{6930}(41,\cdot)\)	6930.hp	30	no	\(-1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{6930}(43,\cdot)\)	6930.fc	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{6930}(47,\cdot)\)	6930.ix	60	no	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(i\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{6930}(53,\cdot)\)	6930.if	60	no	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)	\(e\left(\frac{23}{60}\right)\)
\(\chi_{6930}(59,\cdot)\)	6930.hc	30	no	\(1\)	\(1\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)
\(\chi_{6930}(61,\cdot)\)	6930.hn	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(1\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{30}\right)\)
\(\chi_{6930}(67,\cdot)\)	6930.ex	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{6930}(71,\cdot)\)	6930.dp	10	no	\(-1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{6930}(73,\cdot)\)	6930.ie	60	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{6930}(79,\cdot)\)	6930.hi	30	no	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(-1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{30}\right)\)
\(\chi_{6930}(83,\cdot)\)	6930.jc	60	no	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{6930}(89,\cdot)\)	6930.dj	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{6930}(97,\cdot)\)	6930.ia	60	no	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{6930}(101,\cdot)\)	6930.hh	30	no	\(-1\)	\(1\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{6930}(103,\cdot)\)	6930.iv	60	no	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{6930}(107,\cdot)\)	6930.jb	60	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)	\(e\left(\frac{49}{60}\right)\)
\(\chi_{6930}(109,\cdot)\)	6930.df	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6930}(113,\cdot)\)	6930.jf	60	no	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{59}{60}\right)\)
\(\chi_{6930}(127,\cdot)\)	6930.fk	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{6930}(131,\cdot)\)	6930.bx	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{6930}(137,\cdot)\)	6930.ik	60	no	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{6930}(139,\cdot)\)	6930.gt	30	no	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{14}{15}\right)\)
\(\chi_{6930}(149,\cdot)\)	6930.hb	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)
\(\chi_{6930}(151,\cdot)\)	6930.gd	30	no	\(-1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{5}\right)\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.